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10\times 2-30\times 5=30x\times \frac{7}{10}-15\times 3+30x
Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 30x, the least common multiple of 3x,x,10,2x.
20-150=30x\times \frac{7}{10}-15\times 3+30x
Do the multiplications.
-130=30x\times \frac{7}{10}-15\times 3+30x
Subtract 150 from 20 to get -130.
-130=21x-15\times 3+30x
Multiply 30 and \frac{7}{10} to get 21.
-130=21x-45+30x
Multiply -15 and 3 to get -45.
-130=51x-45
Combine 21x and 30x to get 51x.
51x-45=-130
Swap sides so that all variable terms are on the left hand side.
51x=-130+45
Add 45 to both sides.
51x=-85
Add -130 and 45 to get -85.
x=\frac{-85}{51}
Divide both sides by 51.
x=-\frac{5}{3}
Reduce the fraction \frac{-85}{51} to lowest terms by extracting and canceling out 17.